Problem of the Week 1117
If one thinks of the binary representation of a number as a base-ten number, we can ask: Which numbers are factors of their binary selves?
For instance, 2 is a factor of 10, 10 is a factor of 1010, and 20 is a factor of 10100. If a number has this property (binary divisibility) and I multiply it by 2 or 10, the new product has that property as well.
Aside from powers of 2 and 10, what other numbers have this property? Find at least two.
Is there a pattern we can use to generate some or all of them?
© Copyright 2009 Dave Ehren and Shilad Sen. Reproduced with permission.